Payá, who is using her tour of the United States and Europe to build international pressure for an investigation of the death of her father, Oswaldo Payá, said he and her family had come under increasing death threats before he died.

“The death threats became more frequent, more intense, more chilling,” said Payá, 24, in an interview with Fox News Latino on Tuesday. “I want an independent, international investigation of that accident, of how my father died.”

Payá said she doubts that it is a coincidence that just two months before the accident in July, her father was in another serious car crash on a nearly empty, broad street in Cuba.

“My mother and father were in the car, on a Saturday afternoon,” she said. “There was light traffic, and a car intentionally hit them from behind. They ended up on the opposite side of the highway, the car overturned. By a miracle, they survived.”

Payá said that police arrived almost instantly.

“It was strange how they just appeared out of nowhere and whisked my father and mother away from the scene,” she said. “They moved my parents so quickly that they did not even see who was in the other car or get a good look at it.”

Payá said that the accident could have killed their parents if there had been oncoming traffic.

She said that a Cuban government security agent stood guard outside her father’s hospital room, and that police told the family that an occupant of the other car accused her parents of causing the accident.

“We knew it was no accident,” she said.

Oswaldo Payá received worldwide attention when he launched the Varela Project, which called for a national referendum on free elections, free expression and releasing political prisoners. Payá, who received numerous international human rights awards, including the European Parliament's Sakharov prize, got more than 24,000 signatures on his petition, but the Cuban government has refused to acknowledge it.

Rosa María Payá said that while Raúl Castro’s new policies on relaxing some travel restrictions for Cuba and for private enterprise have come across to some as an step toward making democratic reforms, repression actually is on the rise.

“People who criticize the government, or are seen as a threat to it, are beaten, imprisoned or intimidated,” she said.

Payá’s international campaign for an investigation of her father’s death coincides with growing calls in the United States for such an inquiry.

A bipartisan group of U.S. senators is calling for an investigation, and the editorial boards of some of the largest newspapers in the nation say the fatal car wreck is suspicious and raises serious questions.

The Cuban government has insisted that the wreck resulted from careless driving. But others claim that a second car intentionally rammed the one carrying Payá, and another activist, Harold Cepero, who also died.

Earlier this year, the senators, who include Florida Republican Marco Rubio and New Jersey Democrat Robert Menendez, both sons of Cuban immigrants, signed a letter to the Inter-American Commission on Human Rights of the Organization of American States asking for an investigation.

“Oswaldo Payá was a brave man trying to peacefully advocate for greater political freedom for his fellow Cuban brothers and sisters,” the letter said. “It increasingly looks like he paid for that effort with his life. His memory and his family deserve an honest and independent accounting of what happened. We urge the Commission to undertake this investigation without delay.”

The Cuban government said that Payá died after the car in which he was a passenger skidded into a tree after speeding. Cuban authorities placed the blame on the driver, Angel Carromero, an official of Spain’s Popular Party.

The authorities convicted Carromero, but released him in December, allowing him to serve the rest of his sentence in Spain.

But Carromero was quoted in an interview with The Washington Post earlier this month alleging that a car with Cuban government license plates deliberately hit their car.

Carromero told the Post that a car traveling behind them “began to harass us, getting very close.”

He said: “Oswaldo and Harold told me it must be from ‘la comunista’ because it had a blue license plate, which they said is what the government uses. Every so often I looked at it through the rearview mirror and could see both occupants of the car staring at us aggressively ... Suddenly I felt a thunderous impact from behind.”

Payá’s daughter said that after the fatal wreck, Cuban authorities went to her home to ask her family if they wanted to seek punishment for Carromero.

“We said no. We know that Carromero was also a victim in all of this,” said Payá, who this year appeared before the United Nations Human Rights Council in Geneva and delivered a petition with dozens of signatures of human rights activists and political leaders from around the world seeking an independent investigation of her father’s death.

Payá said her family still is receiving threats.

“They called my house a month ago, saying ‘I’m going to kill you,’” she said, noting that the callers did not identify themselves. “That’s the same thing they would say to my father.”

She and her family feel afraid, but the determination to seek justice for her father and expose human rights violations by the Cuban regime is larger than the fear, she said.

“Our mission is to call for a truly independent investigation,” she said, “and at the same to call global attention to the way the Cuban government will stop at nothing to silence and mistreat its critics and opponents.”

It is how her father raised her to be, she said.

“My father always, somehow, clung to optimism, to hope that Cuba could find happiness and overcome despite the repression,” she said.

“He raised us kids telling us to speak our minds, not to be afraid, and that any teacher or any other authority figure who had a problem with that, he would deal with them,” she said. “It is the kind of freedom many kids in Cuba did not, and still do not, have."

"The common thing in Cuba is for parents to warn them never to repeat any criticism of the government that they hear spoken at home. Many people feel a deep fear in Cuba, and the consequences that they fear are very real.”